4. What Is a Systolic Array?
A systolic array is an arrangement of processors in an array
where data flows synchronously across the array between
neighbors, usually with different data flowing in different directions
Each processor at each step takes in data from one or more
neighbors (e.g. North and West), processes it and, in the next
step, outputs results in the opposite direction (South and East).
H. T. Kung and Charles Leiserson were the first to publish
a paper on systolic arrays in 1978, and coined the name.
5. What Is a Systolic Array?
A specialized form of parallel computing.
Multiple processors connected by short
wires.
Unlike many forms of parallelism which
lose speed through their connection.
Cells(processors), compute data and store it
independently of each other.
6. Systolic Unit(cell)
Each unit is an independent processor.
Every processor has some registers and an
ALU.
The cells share information with their
neighbors, after performing the needed
operations on the data.
8. N-body Problem
Conventional method: N2
Systolic method: N
We will need one processing element for
each body, lets call them planets.
9. B2
B3
B1
B4
B6
B5
Six planets in orbit with different masses, and different forces
acting on each other, so are systolic array will look like this.
10. Each processor will hold the newtonian force formula:
Fij = kmimj/d2ij , k being the gravitational constant.
Then load the array with values.
B1 B2 B3 B4 B5 B6
Now that the array has the mass and the coordinates of
Each body we can begin are computation.
18. Matrix Multiplication
a11 a12 a13 b11 b12 b13 c11 c12 c13
a21 a22 a23
a31 a32 a33 * b21 b22 b23
b31 b32 b33
= c21 c22 c23
c31 c32 c33
Conventional Method: N3
For I = 1 to N
For J = 1 to N
For K = 1 to N
C[I,J] = C[I,J] + A[J,K] * B[K,J];
19. Systolic Method
This will run in O(n) time!
To run in N time we need N x N processing units, in this case
we need 9.
P1 P2 P3
P4 P5 P6
P7 P8 P9
20. We need to modify the input data, like so:
a13 a12 a11
Flip columns 1 & 3 a23 a22 a21
a33 a32 a31
b31 b32 b33
Flip rows 1 & 3 b21 b22 b23
b11 b12 b13
and finally stagger the data sets for input.
21. b33
b32 b23
b31 b22 b13
b21 b12
b11
a13 a12 a11 P1 P2 P3
a23 a22 a21 P4 P5 P6
a33 a32 a31 P7 P8 P9
At every tick of the global system clock data is passed to each
processor from two different directions, then it is multiplied
and the result is saved in a register.
30. Same answer! In 2n + 1 time, can we do better?
The answer is yes, there is an optimization.
23 36 28
25 39 34
28 32 37
P1 P2 P3 P4 P5 P6 P7 P8 P9
23 36 28 25 39 34 28 32 37
31. Cannon’s Technique
No processor is idle.
Instead of feeding the data, it is cycled.
Data is staggered, but slightly different than
before.
Not including the loading which can be
done in parallel for a time of 1, this
technique is effectively N.
32. Other Applications
Signal processing
Image processing
Solutions of differential equations
Graph algorithms
Biological sequence comparison
Other computationally intensive tasks
33. Samba: Systolic Accelerator
for Molecular Biological
Applications
This systolic array contains 128 processors shared into 32 full custom
VLSI chips. One chip houses 4 processors, and one processor performs
10 millions matrix cells per second.
34. Why Systolic?
Extremely fast.
Easily scalable architecture.
Can do many tasks single processor
machines cannot attain.
Turns some exponential problems into
linear or polynomial time.
35. Why Not Systolic?
Expensive.
Not needed on most applications, they are a
highly specialized processor type.
Difficult to implement and build.
Notas del editor
I thought it was interesting enough to point out that the term Systolic actually refers to Systole which essentially means the “rhythmic beating of the heart.” This is appropriate because of the way a systolic array fans in values and relies on them being in a specific place at a specific time so that they can be “pumped” through the system.
